Practical Formulas to Calculate Suspender Tension Based on Frequency

In order to analyze the influence of frequency on suspender tension, a partial differential equation of motion is established for the suspender according to its vibration mechanical properties and dynamic equilibrium. Then, a computational formula for the frequency and suspender force is built taking into account the influence of flexural rigidity, rotational inertia, shear deformation, and the coupling of rotational inertia and shear deformation. Comparing frequencies of different orders and fitting frequency difference for various lengths of suspenders leads to the finding that the fundamental frequency worked out using high-order differential frequency will contain a positive error and thus causes a positive deviation in the cable force. On this basis, the modified value for the first-order frequency is then obtained and practical formulas for calculating the cable force are proposed. In a case study, the proposed formulas are compared with the string vibration formula and the formula that takes the bending stiffness into consideration. The result show that using the practical formulas, the error between the calculated suspender tension and the measured value is no more than 5%, which validates the practical formulas.